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MathNet 2018-part-05 — 181 problems (EN–VI) Question 144

Math Olympiad Vault · MathNet 2018-part-05 — 181 problems (EN–VI)

Question 144

Simplify the expression:
$$
2\left(x y^{-1}-1\right)^{-p}\left(x^{2} y^{-2}-1\right)^{p}-\left(\frac{x+y}{y}\right)^{p}
$$
Compute the value of the expression for $x=-2$, $y=-\frac{1}{2}$ and $p=-3$.